Critical angle of incidence

TXRF can be used to determine the contamination present on, in, and below the wafer surface (see Fig. 16). Changing the angle of incidence, while remaining below the critical angle of incidence, reveals the nature of the... 

Classical and quantum treatments of electromagnetic fields [7], near a plane dielectric interface, show that the probability of photo-ionization or photo-excitation of an atom exhibits a pronounced peak at the critical angle of incidence of a plane wave propagating in the dense medium. The probability of absorption or emission of a photon is proportional to the photometric intensity of the electromagnetic field. In particular, consider a plane wave propagating in the dense medium with refractive index /2i, at angle of incidence Ox. The intensity of the transmitted field at a distance dy from the interface is given by... 

Absorption coefficient in the organic phase Penetration depth of light Critical angle of incidence... 

This relationship ensures that the critical angle of incidence of the interface is not exceeded and that total internal reflection occurs (Levi, 1980). Typical values of NA for fused SiOj fibers with polymer cladding are in the range of 0.36-0.40. The typical values of = 14° used to insert the beam of the biomedical laser into the fiber is much smaller than those values ( 21-23°) corresponding to typical NA values. The maximum value of the propagation angle a typically used in biomedical laser systems is i 4.8°. 

Light is transmitted from one end of an optical fiber to the other by total internal reflection (TIR) as illustrated in Figure 32.15. Modern optical fibers use a composite construction with a core of refractive index rii and a cladding with a lower refractive index, Hi, such that ( i - tii) is typically in the range of 0.005-0.05. Light will remain in the fiber when the critical angle of incidence, is met or exceeded. To determine L we make use of Snell s law (which can be derived from Maxwell s equations) ... 

When i is less than 1 there will exist a critical angle above which the angle of refraction will be real for all incident angles. (Note that, apart from light water and compounds that are heavily hydrogenous, most materials encountered in polymer science have a positive A and thus i < 1). At this critical angle of incidence, 0c, 0i is zero and... 

Total reflection n. When light passes from any medium to one in which the velocity is greater, refraction ceases and total reflection begins at a certain critical angle of incidence of 9 such that... 

When n is less than 1 there will exist a critical angle above which the angle of reflection will be real for all ineident angles. At this critical angle of incidence. 

In a variation of the above method Wright et al. [21] detected the component of the incident beam that was reflected from the immersed specimen and hence measured the critical angle of incidence. 

In the reflectivity technique, the intensity of specularly reflected x-rays is measured as a function of the incidence angle. Since the reflection coefficient for x-rays is less than unity, it is totally reflected from the sample surface, up to the critical angle of incidence. This critical angle is proportional to the square root of electron density and, hence, of the mass density. The density measured in this way can be used to derive the sp lsp ratio or, said otherwise, the extent to which a film is graphite like (p = 2.25 g/cm ) or diamond like (p = 3.51 g/cm ). The results of a study of the density variation with the time of deposition of diamond-like films (converted to film thickness) in the initial stages of their growth can be found in Ref. 71. 

Fig. 4.48. Principle of the Wolter type I X-ray telescope the telescope focus is at Fs, and the focus of the paraboloid is at the second focus of the hyperboloid. The convergences are considerably exaggerated and the surfaces actually resemble ordinary cylinders. The critical angle of incidence, usually less than 1°, depends on the mirror material, refraction index, and on the wavelength of the incident radiation. The paraboloid is in effect a primary mirror and the hyperboloid is a secondary that is added to shorten the optical path and correct for aberrations such as coma...

More precise measurements can be obtained with commercial refractometers, such as an Abbe or Pulfrich. Both refractometers are based on measuring the critical angle of incidence between the specimen and a standard prism. The sample consists of a flat plate with one surface and an adjacent vertical edge well pohshed. The contact between the polished sample and the prism is enhanced with an approximately matching index oU. A split image is adjusted to coincide, and the refractive index is read directly. The precision here is generally of the order 10". ... 

At the extremely short wavelengths of X-radiation, total reflection only occurs at glancing incidence. Copper radiation has a critical angle of incidence for total reflection of 1 r for glass and 30 for a gold surface. Most of the shorter wavelength radiation passes through the reflector. However, it is prudent to use a nickel filter prior to the mirrors to reduce the Kp component. 

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